Notes on $\log(ζ(s))^{\prime\prime}$

Jeffrey Stopple

Published 2013-11-21, updated 2014-12-22Version 2

Motivated by the connection to the pair correlation of the Riemann zeros, we investigate the second derivative of the logarithm of the Riemann zeta function, in particular the zeros of this function. Theorem 1 gives a zero-free region. Theorem 2 gives an asymptotic estimate for the number of nontrivial zeros to height T. Theorem 3 is a zero density estimate.